1. Read the assignment description in the attached PDF of the same name.
2. Upload an MS Word or PDF file containing the roots of the polynomial x^3-3x^2+x-3 found by your user-defined function CUBIC.
3. Upload code (.sas file) used to produce the print out in step 2.

Incase the file NEWTONS_METHOD Doesn't open, the code is here:

proc iml;
/** x##3 - 2 x##2 -4 x + 3 **/
q = {1, -2, -4, 3};

start eval(p,x,val);
N = NROW(p);
val = p[1];
do k = 1 to N-1;
val = val*x + p[k+1];
end;
finish eval;

start der(p,p_prime);
p_prime = J(NROW(p)-1,1,0);
do k = 1 to NROW(p) - 1;
p_prime[k] = (NROW(p)-k)*p[k];
end;
finish der;

start newton(q,x0,tol,root);
/* The value x0 is the initial estimate of the root.
The value tol is how close to zero the polynomial should be to for the current 
estimate to be accepted as a root.*/

call der(q,q_prime);
iter_max = 100;
xnext = x0;
do k = 1 to iter_max;
call eval(q,xnext,val_1);
if abs(val_1) < tol then k = iter_max;
call eval(q_prime,xnext,val_2);
xnext = xnext - val_1/val_2;
end;
root = xnext;
finish newton;

call newton(q,0,0.0001,r1);
print r1;

/*Try a different starting value ..*/

call newton(q, 2.5,0.0001,r2);
print r2;

call newton(q, -7,0.0001,r3);
print r3;

/* Compare with the roots obtained using the built-in function. */

roots = polyroot(q);
print roots;
quit;
run;